Around here, we call this "pillow bread."
The first time I brought it home from the market, Dan called it that and said he wanted a pita big enough to sit in like beanbag chair. It really is that soft.
It's baked by Global Bakeries, Inc. in Pacoima. I buy mine at Valley Produce in Reseda, CA.
I'm toasting little pita triangles right now to eat with the rest of the Spicy Squash Taco stuff we had for dinner. (More on that tomorrow!)